2. Benchmark solution

2.1. Normal force in cables according to ETCC

The reference solution for models A and B was obtained by an Excel spreadsheet created by the company GDS.

The two models correspond to two methods of calculating the loss of prestress due to the relaxation of steels.

• In modeling A, relaxation losses are considered while neglecting elastic losses (direct calculation with DEFI_CABLE_BP) i.e.:

\({F}_{i}(s)\mathrm{=}{F}_{0}{\mathrm{exp}}^{\mathrm{-}\mu (\theta +ks)}\mathrm{-}\text{recul d'ancrage}\)

and finally:

\(F(s)\mathrm{=}{F}_{i}(s)\mathrm{-}\mathrm{0,66}{\rho }_{1000}\text{.}{\mathrm{exp}}^{\mathrm{9,1}{F}_{i}(s)\mathrm{/}{F}_{\mathit{prg}}}\text{.}{(\frac{t}{1000})}^{\mathrm{0,75}(1\mathrm{-}{F}_{i}(s))\mathrm{/}{F}_{\mathit{prg}}}\text{.}{10}^{\mathrm{-}5}{F}_{i}(s)\)

• In modeling B, the relaxation losses of steels are calculated from the tension taking into account the elastic losses obtained by a previous calculation, where the cables were put under tension in 2 groups, i.e.:

for group 1 (odd cables):

\({F}_{i}^{1}(s)\mathrm{=}{F}_{0}{\mathrm{exp}}^{\mathrm{-}\mu (\theta +ks)}\mathrm{-}\text{recul d'ancrage}\mathrm{-}\frac{{A}_{p}{E}_{p}\Delta {\sigma }_{c}(x)}{E}\)

for group 2 (even cables):

\({F}_{i}^{2}(s)\mathrm{=}{F}_{0}{\mathrm{exp}}^{\mathrm{-}\mu (\theta +ks)}\mathrm{-}\text{recul d'ancrage}\)

and \(F(s)={F}_{i}^{\mathrm{1,2}}(s)-\mathrm{0,66}{\rho }_{1000}\text{.}{\mathrm{exp}}^{\mathrm{9,1}{F}_{i}^{\mathrm{1,2}}(s)/{F}_{\mathit{prg}}}\text{.}{\left(\frac{t}{1000}\right)}^{\mathrm{0,75}(1-{F}_{i}^{\mathrm{1,2}}(s))/{F}_{\mathit{prg}}}\text{.}{10}^{-5}{F}_{i}^{\mathrm{1,2}}(s)\)

The reference value a was actually obtained by considering that there were the same elastic losses on all cables worth \(\Delta {F}_{\mathit{el}}(s)\mathrm{=}\frac{{A}_{p}{E}_{p}\Delta {\sigma }_{c}(x)}{2E}\).

2.2. Fracture modeling

For the C modeling, the tension profile was postulated in a completely arbitrary manner. We simply check that the result at the end of the prestress is equal to the profile that we wanted to introduce.